The biggest reason that cities are expensive to live in isn't so much a lack of land, it's a lack of properly zoned land. Even in limited areas like Manhattan,

The biggest reason that cities are expensive to live in isn't so much a lack of land, it's a lack of properly zoned land. Even in limited areas like Manhattan, we have imposed extra artificial limitations on ourselves in the form of zoning laws. Remove those laws, and there will be much more housing built, and it will be cheaper to live in cities. Forced low income housing is another restriction, by only giving developers reasonable exceptions to draconian laws like minimum parking requirements if they set aside a certain portion of the units to low income housing, the government again restricts density. Better to remove ridiculous zoning laws in general, and housing will become more affordable for everyone.